Question

If $A+B=\frac{\pi }{2}$, find the value of $\sin A\cos B+\cos A\sin B$

• A. $0$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

Answer: (B)

$1$

We know that $\sin A\cos B+\cos A\sin B=\sin (A+B)$
Given, $A+B=\frac{\pi }{2}$
So, $\sin A\cos B+\cos A\sin B=\sin (A+B)=\sin \frac{\pi }{2}=1$